Is 31000 a prime number?

No. 31000 is composite — it has more than 2 divisors (it has 32).

Divisors of 31000: All 32 Factors

Q: What are the divisors of 31000?

The divisors (factors) of 31000 are 1, 2, 4, 5, 8, 10, 20, 25, 31, 40, 50, 62, 100, 124, 125, 155, 200, 248, 250, 310, 500, 620, 775, 1000, 1240, 1550, 3100, 3875, 6200, 7750, 15500, 31000.

Q: What is the sum of the divisors of 31000?

The sum is 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 31 + 40 + 50 + 62 + 100 + 124 + 125 + 155 + 200 + 248 + 250 + 310 + 500 + 620 + 775 + 1000 + 1240 + 1550 + 3100 + 3875 + 6200 + 7750 + 15500 + 31000 = 74880.

Quick Answer

31000 has 32 divisors (factors): 1, 2, 4, 5, 8, 10, 20, 25, 31, 40, 50, 62, 100, 124, 125, 155, 200, 248, 250, 310, 500, 620, 775, 1000, 1240, 1550, 3100, 3875, 6200, 7750, 15500, 31000.

Sum: 74880.

Divisors (Factors) Calculator

Divisors Multiples Prime Factoriz. GCF LCM

Use the calculator above to find all divisors (also called factors) of any positive integer up to 4,782,969. Beyond the divisor list, this tool also shows divisor pairs, the sum and count of divisors, prime factorization, and number properties (prime, perfect square, perfect number).

All Divisors of 31000

The number 31000 has 32 divisors:

1, 2, 4, 5, 8, 10, 20, 25, 31, 40, 50, 62, 100, 124, 125, 155, 200, 248, 250, 310, 500, 620, 775, 1000, 1240, 1550, 3100, 3875, 6200, 7750, 15500, 31000

Divisor Pairs of 31000

Each pair multiplies to 31000:

Factor 1	×	Factor 2	=	Product
1	×	31000	=	31000
2	×	15500	=	31000
4	×	7750	=	31000
5	×	6200	=	31000
8	×	3875	=	31000
10	×	3100	=	31000
20	×	1550	=	31000
25	×	1240	=	31000
31	×	1000	=	31000
40	×	775	=	31000
50	×	620	=	31000
62	×	500	=	31000
100	×	310	=	31000
124	×	250	=	31000
125	×	248	=	31000
155	×	200	=	31000

Number of Divisors

The number 31000 has 32 divisors, written as τ(31000) = 32 in number theory.

Sum of Divisors

σ(31000) = 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 31 + 40 + 50 + 62 + 100 + 124 + 125 + 155 + 200 + 248 + 250 + 310 + 500 + 620 + 775 + 1000 + 1240 + 1550 + 3100 + 3875 + 6200 + 7750 + 15500 + 31000 = 74880

Prime Factorization of 31000

See the full prime factorization calculator →

Properties of 31000

31000 is composite.
31000 is not a perfect square.
Number of divisors: 32.
Sum of divisors: 74880.

Common Divisors with Another Number?

Looking for the divisors that 31000 shares with another number? Use our Greatest Common Factor (GCF) calculator — it finds all common divisors and the largest one.

Step-by-Step: How to Find the Divisors of 31000

An efficient way to find divisors uses the complementary pair trick: check each integer i from 1 to √31000 ≈ 176.07. If i divides 31000, then both i and 31000/i are divisors.

1 divides 31000 (31000 ÷ 1 = 31000) → pair (1, 31000)
2 divides 31000 (31000 ÷ 2 = 15500) → pair (2, 15500)
4 divides 31000 (31000 ÷ 4 = 7750) → pair (4, 7750)
5 divides 31000 (31000 ÷ 5 = 6200) → pair (5, 6200)
8 divides 31000 (31000 ÷ 8 = 3875) → pair (8, 3875)
10 divides 31000 (31000 ÷ 10 = 3100) → pair (10, 3100)
20 divides 31000 (31000 ÷ 20 = 1550) → pair (20, 1550)
25 divides 31000 (31000 ÷ 25 = 1240) → pair (25, 1240)
31 divides 31000 (31000 ÷ 31 = 1000) → pair (31, 1000)
40 divides 31000 (31000 ÷ 40 = 775) → pair (40, 775)
50 divides 31000 (31000 ÷ 50 = 620) → pair (50, 620)
62 divides 31000 (31000 ÷ 62 = 500) → pair (62, 500)
100 divides 31000 (31000 ÷ 100 = 310) → pair (100, 310)
124 divides 31000 (31000 ÷ 124 = 250) → pair (124, 250)
125 divides 31000 (31000 ÷ 125 = 248) → pair (125, 248)
155 divides 31000 (31000 ÷ 155 = 200) → pair (155, 200)
Collect all unique values: {1, 2, 4, 5, 8, 10, 20, 25, 31, 40, 50, 62, 100, 124, 125, 155, 200, 248, 250, 310, 500, 620, 775, 1000, 1240, 1550, 3100, 3875, 6200, 7750, 15500, 31000} — total 32 divisors.
Sum: 1 + 2 + 4 + 5 + 8 + 10 + 20 + 25 + 31 + 40 + 50 + 62 + 100 + 124 + 125 + 155 + 200 + 248 + 250 + 310 + 500 + 620 + 775 + 1000 + 1240 + 1550 + 3100 + 3875 + 6200 + 7750 + 15500 + 31000 = 74880.

Nearby Examples

n	divisors count	sum σ(n)
360	24	1170
240	20	744
180	18	546
144	15	403
120	16	360
100	9	217
90	12	234
84	12	224

Related Operations for 31000

Multiples of a Number — "outward" complement of divisors
31000 Prime Factorization — decompose into prime building blocks
Find GCF of 31000 and another number
Find LCM of 31000 and another number
Is 31000 a perfect square? (odd divisor count ⇔ yes)

What Is a Divisor?

A divisor (also called a factor) of a positive integer n is any positive integer d such that n ÷ d has no remainder. In other words, d divides n evenly.

Every positive integer n has at least two divisors: 1 and n itself (with 1 being the trivial case of having only itself). Numbers with exactly 2 divisors are prime; numbers with 3 or more divisors are composite.

Why use this calculator? Beyond just listing divisors, this tool computes the sum σ(n), the count τ(n), prime factorization, divisor pairs (useful for visual learners and factoring problems), and detects whether n is a prime, a perfect square, or a perfect number.

References

Divisors Calculation Examples

Find all divisors of these numbers:

Related Calculators

Multiples of a Number — "outward" complement
Prime Factorization — product of prime divisors
Greatest Common Factor (GCF) — largest common divisor of 2+ numbers
Least Common Multiple (LCM) — smallest common multiple
Is N a Perfect Square? — odd divisor count check